Based on the Asus web site, your motherboard supports up to 24GB of RAM.
RAM is installed in pairs, so you need to match the RAM modules you install so if you install 4GB in one slot, you need to install a matching 4GB module in the corresponding slot. You can't have, for example, one slot at 2GB and it's matching slot having a 4GB stick.
You would need to see what slots are currently being used. Based on the mainboard and the amount of RAM you report it has, it sounds like the existing RAM modules are either 1GB (1 in each slot) or 3 x 2GB modules (3 slots occupied.)
Yes, the mainboard supports RAM modules running at those speeds. For best results, all RAM you install should have matching speeds (ie. 1600 or 1333 etc) and this is especially important if you are matching memory in the individual slots. Eg. If you had one stick of 4GB running at 1333, you would need to get another stick running at 1333 for the corresponding slot to get the 8GB's of RAM working (a mismatch of the speed can result in the system not booting up due to the mismatch.) While you could have one pair with 1333 and another at 1600, the system would run at the speed of the slower RAM.
Your Operating System will also need to be able to support the amount of RAM you want to install, if your operating system is a 64 bit version then you would be able to access the additional memory - based on the fact that you report it has 6GB of RAM, I am presuming your OS is 64 bit.
If you wanted to retain your existing RAM, then you'd need another 2GB stick that matches the existing RAM module to ensure you have your slots paired up - this would take you up to 8GB. Another 2 x 2GB sticks would give you 12GB.
Or you could get entirely new sticks to replace the existing modules (3 x 4GB sticks would give you 12 GB, 4 x 4GB (2 pairs loaded) gives you 16GB, 6 x 4GB would give you 24GB, the maximum your mainboard supports.
How many modules do you have to get those 6 GB? – Seth – 2016-12-15T08:30:41.340
@Seth, I currently have 3. – w0051977 – 2016-12-15T08:31:26.373